Calculate the median from the following data:
Height - (in cm) | 135 - 140 | 140 - 145 | 145 - 150 | 150 - 155 | 155 - 160 | 160 - 165 | 165 - 170 | 170 - 175 |
No. of boys | 6 | 10 | 18 | 22 | 20 | 15 | 6 | 3 |
To find median, Assume
Σfi = N = Sum of frequencies,
h = length of median class,
l = lower boundary of the median class,
f = frequency of median class
and Cf = cumulative frequency
Lets form a table.
HEIGHT(cm) | NUMBER OF BOYS(fi) | Cf |
135 - 140 | 6 | 6 |
140 - 145 | 10 | 6 + 10 = 16 |
145 - 150 | 18 | 16 + 18 = 34 |
150 - 155 | 22 | 34 + 22 = 56 |
155 - 160 | 20 | 56 + 20 = 76 |
160 - 165 | 15 | 76 + 15 = 91 |
165 - 170 | 6 | 91 + 6 = 97 |
170 - 175 | 3 | 97 + 3 = 100 |
TOTAL | 100 |
So, N = 100
⇒ N/2 = 100/2 = 50
The cumulative frequency just greater than (N/2 = ) 50 is 56, so the corresponding median class is 150 - 155 and accordingly we get Cf = 34(cumulative frequency before the median class).
Now, since median class is 150 - 155.
∴ l = 150, h = 5, f = 22, N/2 = 50 and Cf = 34
Median is given by,
⇒
= 150 + 3.636
= 153.64
Thus, median is 153.64 cm.